Sure they do. Cash only might be a misnomer. The idea is they don't take insurance, so don't have to have a team of administrators and accountants to navigate the system to get payed. The costs can be outlined for patients beforehand when you don't have to deal with the government or insurance companies.
It's a system that's been working great for rich people for years, these guys seem to be more targeting middle to upper middle class, which is great. Of course it's not a fix all because poor people still wouldn't be able to afford their care, but no system is a fix all. More options is almost always a good thing.